Solve 9(16)^2x=589824

$$9 ( 16 ) ^ { 2 x } = 589824$$

Solve for x

$$x=2$$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$9\times 16^{2x}=589824$$

Divide both sides by 9.

$$16^{2x}=65536$$

Take the logarithm of both sides of the equation.

$$\log(16^{2x})=\log(65536)$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$2x\log(16)=\log(65536)$$

Divide both sides by \log(16).

$$2x=\frac{\log(65536)}{\log(16)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$2x=\log_{16}\left(65536\right)$$

Divide both sides by 2.

$$x=\frac{4}{2}$$

Solve for x (complex solution)

$$x=\frac{\pi n_{1}i}{4\ln(2)}+2$$

$$n_{1}\in \mathrm{Z}$$